1. Field of the Invention
This invention relates to methods and apparatus for measurements of displacements or velocities of particle fields from double-exposure particle images or holograms.
2. Description of the Related Art
In application areas such as aircraft and automobile design, chemical, material, drug and food manufacture, environmental control, power generation, and biomedical engineering, there is a ubiquitous need to measure three dimensional velocity fields in turbulent, complex fluid flows. Such information is critical to the modeling and control of various flows of technological importance.
In many such applications, measurement of the displacement of small markers/tracers (either particles or speckles) in full field is required. Such full-field measurement capability was lacking until the establishment and commercialization of the Particle Image Velocimetry (PIV) technique a few years ago. In the PIV technique, a pair of images is captured within a short time interval, and the particle displacement from the two images is computed. The time interval is chosen so that the displacement during that time period is small enough to approximate the instantaneous velocity. Applications of this sort of velocimetry include deformation gauging of speckle-sprayed surfaces of deformable solid objects, velocity measurement of the discrete phase (solid particles, droplets, and bubbles) in a two-phase flow, and continuous-phase fluid flows seeded with particles.
For these applications, variation in the local densities of tracer particles presents a problem. Commercial instruments like PIV use Fast Fourier Transform (FFT)-based correlation to estimate the degree of displacement of a small group of tracer particles; in fact, FFT-based correlation is the only correlation technique available in commercial systems. Since velocity vectors obtained using FFT-based correlation are based on average over groups of tracer particles, information about individual particles is lost, resulting in a limited spatial resolution for the extracted velocity field. Where particles are especially sparse, FFT-based correlation methods fail completely; such local inhomogeneities, however, are unavoidable in complex, turbulent flows.
PIV measurements are limited to two planes. For truly three dimensional flow field measurements, it is necessary to use Holgraphic Particle Image Velocimetry (HPIV), a new technique currently under development at several leading laboratories around the world, including the Laser Flow Diagnostics Laboratory at Kansas State University. HPIV works by recording the instantaneous 3-dimensional images of a large quantity of tracer particles in a fluid volume recorded on a hologram, and then reconstructing the particle images optically. The instantaneous volumetric velocity field can be retrieved by finding the displacements of the particles in the image volume during the period between exposures. Applied in conjunction with cinematography, simultaneously time- and space-resolved measurements in three dimensions are possible.
In practice, a number of serious issues stand in the way of the commercial use of HPIV for measuring three-dimensional fluid motion. HPIV configurations are broadly classifiable, based on the holographic system, as either xe2x80x9cin-linexe2x80x9d or xe2x80x9coff-axisxe2x80x9d. In in-line systems, only one beam is employed to produce both the object wave (scattered component) and the reference wave (unscattered component). While the optical geometry of in-line systems is simple enough for use in commercial systems, in-line HPIV systems suffer from speckle to an extent which makes it impossible to resolve particle images in sufficient detail for most commercial applications. Furthermore, in-line particle images are formed with an extremely narrow forward scattering lobe. Due to such small Numerical Aperture (N.A.), the particle images suffer from large depth of focus. Off-axis systems produce holograms with better SNR, at the expense of simplicity of optical geometry. Many variations on the themes of in-line versus off-axis imaging systems are possible, so that the distinction between them can become blurred.
Finally, a major challenge to commercial HPIV applications has been the magnitude of the data processing task. The amount of data being processed at a given time is exorbitantly large, and particularly so in the case of HPIV. The data volume one needs to address is typically on the order of 100 Gigabytes with FFT-based methods, which utilize the full three-dimensional volume. Such a large volume of data cannot be processed fast enough, or stored at an acceptable cost for velocity extraction; thus the advent of HPIV demands a more efficient solution to the data storage and processing problem. Ongoing research in the area of PIV data processing has focused on addressing these problems with sophisticated techniques, such as neural nets, fuzzy logic, and genetic algorithms, but these methods have not yet met with practical success.
In standard FFT-based cross-correlation methods the displacement estimate is obtained by applying FFTs to both a target window (for two dimensional PIV systems) or cube (for three dimensional HPIV systems) and a search window or cube. The cross correlation is then calculated in the frequency domain by multiplication, and inversion of the result gives the location of the correlation peak. One disadvantage of this method is that the correlation peak is the optimal displacement for the particles based on mean group displacement throughout the target and search windows/cubes; this means that finer particle displacement data are unrecoverable by this method. In fact, FFT-based correlation may fail completely in windows or cubes where the seeding density is low. Most importantly, the quantity of data to be handled in the case of HPIV excludes the use of FFT-based correlation methods; a typical 100-Gigabyte block of data would take thousands of hours to process by this means. New data processing techniques are therefore demanded, which require less computational power and less data storage capacity.
Space domain cross-correlation methods for PIV and HPIV, which have been researched but have not been commercially implemented, may require the calculation of particle centroids. Various approaches to the problem of finding particle centroids have been taken; most try to minimize computation. In one such implementation, the entire image is scanned, and pixels with intensity higher than a specified threshold are set aside for further computation (the threshold is determined adaptively from the image histogram). For each eligible pixel, a list of preexisting centroids is scanned; if the new pixel is sufficiently close to a preexisting pixel, then the pixels are combined by intensity-weighted averaging to form a new centroid. If the new pixel is isolated, it is added to the list of particle centroids.
No system currently available is capable of processing particle fields for velocimetry in an efficient manner, while retaining the ability to track specific particles. A need remains in the art for such a system.
A number of obstacles have prevented HPIV from becoming reliable and practical. Hence, despite a need in several industries for 3D flow measurements, commercial HPIV systems have not been available.
A need also remains in the art for a workable optical configuration for HPIV, which combines the simplicity of in situ reconstruction with high image quality and easy optical access.
A need also remains in the art for a data processing system which takes full advantage of the 3D holographic images, handles the large quantity of 3D data involved, and delivers particle information and velocity fields efficiently.
It is an object of the present invention to provide a holographic particle imaging system that is capable of extracting three-dimensional detail from the flow field, including but not limited to individual particle sizes, shapes, displacements, velocities and concentrations.
Another object of the present invention is to provide a workable optical configuration for HPIV, which combines the simplicity of in situ reconstruction with high image quality and easy optical access. The present HPIV configuration""s 90-degree scattering feature permits optical access approaching that of planar PIV, which has been widely accepted.
A further object of the present invention is to provide a system with high compression ratios for the data to be processed, together with an efficient velocity field extraction algorithm. The use of particle centroids for velocity field extraction, rather than the image data extracted from the hologram as is used in some HPIV systems, permits the use of less storage and active memory, which speeds the processing of the data. Furthermore, retaining the spatial locations of the particle centroids permits particle pairing to be done after extraction of the major features of the flow; clearly this provides the best possible resolution of the velocity vector field.
To achieve these objects, there is provided a system for the holographic recording of three-dimensional images of a fluid seeded with particles, and for the extraction of the velocity vector field defined by the motion of the fluid. The system includes the specification of an off-axis holographic system utilizing 90-degree scattering to obtain low depth of focus and high SNR, in situ reconstruction of the time-separated holograms, extraction of the particle centroid locations from the time-separated holograms, and a velocity field extraction algorithm which uses particle centroid data, rather than digital images captured from the hologram, to perform the correlations needed to calculate the three-dimensional velocity vector field.
The system utilizes an object beam and two reference beams that are directed onto the holographic recording medium from different reference angles. The different reference angles permit the particle fields recorded at different points of time, t1 and t2=t1+dt, to be unambiguously distinguished from each other. The object wave is obtained by directing a third coherent wavefront at an angle perpendicular to the vector between the particle field and the single recording medium, so that the 90-degree scattering component from this beam interferes with first one reference beam at time t1, and then the other reference beam at time t2=t1+dt. The use of two angularly separated reference waves permits the time-separated holograms to be recorded on a single holographic recording medium. This system geometry results in an improved Numerical Aperture and depth of focus, allowing three-dimensional information to be effectively extracted from the resulting holograms.
The complexity of the imaging system is somewhat ameliorated by the in situ reconstruction scheme, which uses substantially the same optics for reconstruction of the time-separated holograms. The two reference beams are recreated in exactly the same geometry used for recording; the holographic recording medium is placed in the same position with the emulsion facing in the opposite direction, so that the incident reference waves are effectively the phase-conjugates of the original reference waves. The object wave is not needed in the reconstruction process, and so is blocked. The reconstructed images are displayed alternately, on the opposite side of the holographic emulsion, by illuminating the emulsion alternately with the two reference beams.
The system then utilizes an imaging system which alternately interrogates the three-dimensional volumes reconstructed by the two reference beams. A CCD camera on a three-dimensional traverse system, with a small depth of focus, is and acquires planar images by scanning synchronized with the laser. The CCD camera alternately extracts intensity data from the two holograms, taking a thin slice in the depth dimension, and small areas in the planar dimension. This gives rise to a natural three-dimensional grid on each volume. The processor then employs standard particle centroid extraction algorithms to save the three-dimensional location of each particle centroid in the intensity map. The concise cross correlation algorithm (CCC) is then utilized to extract a velocity vector field defined on this grid.
CCC extracts velocity vector fields by measuring displacement in 2-dimensional and 3-dimensional media, including, but not limited to, fluid flows. In the preferred embodiment, particle centroid coordinates are extracted from each pair of images, or from image planes in the hologram. The coordinates alone are retained in the processing that follows, saving both compute time and memory. The first cube is naturally broken into target windows (cubes) by the volume interrogation process. These cubes are sufficiently small that their velocity fields are roughly constant at that scale. The correlation of each window (cube) with a region in the second image (cube) is calculated. The correlation is calculated on the basis of particle centroids alone, with correlation intensities between individual particles being calculated as a decreasing function of distance. Translations are calculated by manipulating centroid coordinates.
To accelerate computation, three 1-dimensional correlations are calculated in place of a complete 3-dimensional correlation. The velocity vectors are obtained by combining x-, y-, (z-) components obtained from the individual correlations. The highest possible spatial resolution can then be obtained, if desired, by translating the images by the extracted velocity and pairing particle centroids individually.
The entire computation can be performed in integer arithmetic only, which means that CCC can be implemented easily on hardware platforms for real-time applications. The method is robust, and much faster than the FFT-based methods in common use.